{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "from scipy import integrate\n",
    "import seaborn as sns\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.set_style(\"white\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the relation between $M_x$ and $h$ when $J$ is fixed to 1 and $h$ varies from 0 to 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "npload = np.load('ising_mx_vs_h.npz')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "h_list = npload['h_list']\n",
    "mx_list = npload['mx_list']\n",
    "energy_list = npload['energy_list']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Analytical calculation of M_x for comparision\n",
    "def calc_m_x(h, j=1):\n",
    "    def calc_big_lambda(lambda_, k):\n",
    "        return np.sqrt(1 + lambda_ ** 2 + 2 * lambda_ * np.cos(k))\n",
    "    lambda_ = np.divide(j, 2 * h) # avoid zero division\n",
    "    L_0 = 1 / np.pi * integrate.quad(lambda k: 1 / calc_big_lambda(lambda_, k), 0, np.pi)[0]\n",
    "    L_1 = 1 / np.pi * integrate.quad(lambda k: 1 / calc_big_lambda(lambda_, k) * np.cos(k), 0, np.pi)[0]\n",
    "    m_x = 1 / 2 * (L_0 + lambda_ * L_1)\n",
    "    return m_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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uISrqWlKRlmT8nchV80Eoshdzqb34V9hLSqe9pHgcAmynQbzdvbkn+B7bo9Az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\n0iGEEEIInZCkQwghhBA68X912bVYI0q4mAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2387b0fee48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(h_list, mx_list, label='SimpleMPS')\n",
    "analytical_h_list = np.linspace(h_list.min(), h_list.max(), 100)\n",
    "plt.plot(analytical_h_list, np.frompyfunc(calc_m_x, 1, 1)(analytical_h_list), label='Analytical (PBC)')\n",
    "plt.xlabel('$h$')\n",
    "plt.ylabel('$M_x$')\n",
    "plt.title('Relation between $M_x$ and $h$ when $J$ is fixed to 1 in TFI model')\n",
    "plt.legend(loc='lower right')\n",
    "plt.savefig('../Img/ising1.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TpToREZEs2rYNnnkGYmPhk0+gfXtXVyTZRS1OIiIimZSYCG++CY0bQ4UKZgdw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\nTgAAhYQTAEAh4QQAUEg4AQAU+gaDB4oagZF5PgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2387bea1d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(h_list, -energy_list)\n",
    "plt.xlabel('$h$')\n",
    "plt.ylabel('Energy')\n",
    "plt.title('Relation between average site energy and $h$ when $J$ is fixed to 1 in TFI model')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the phase diagram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "npload = np.load('ising_phase_diagram.npz')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mx_result = npload['mx_result']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mz_result = npload['mz_result']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "j_grid = npload['j_grid']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "h_grid = npload['h_grid']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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gEJmDREKKjCah4Een/Anur9Nu1RxEkBfBbV4cqYQtfbSEQJtaMDdFEbLuQyCB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\nBIIgCIIgmPw/81M0oUxRdhAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2387be700b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.contourf(j_grid, h_grid, mx_result, np.arange(-0.5, 0.5, 0.01))\n",
    "plt.xlabel('$h$')\n",
    "plt.ylabel('$J$')\n",
    "plt.title('$M_x$ of TFI model')\n",
    "plt.colorbar()\n",
    "plt.savefig('../Img/ising2.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qtQY932q1hkxBDIZBAtEQUBcwegC9v/uiMWhXSP+6BBPksLtCKpLjnIGCp+UE\njGmzLtI7GmKBUw1A2FbMgaWPgesRONVAo0lWVhYMBgOqq6tx5ZVXAgCqqqqQnZ0ddN3cuXNDyiKX\nLFmCn/70p1iwYAEAICcnB4cPH0ZhYSEAoKmpCc3NzZg7d27E42GQQDQERI8bktEDyeDFpb3H1CkH\nXb91CX37OCiiCGEUtGgO2cyqXytm/1SDdjpgPYJLdjOLQKOKxWLB0qVLUVpaio0bN6KlpQXl5eXY\ntGkTADUTMG7cOJjNZkybNi3k/tTUVEycOBEAsGzZMtxzzz2YO3cusrOzsXHjRixevBgZGRkRj4dr\nEoiGgLu3FNLudaDTJ8GueMKWQopWPbxtIhRb56gphdSmGuwdUNptkNu7w+76aNMBdvjQobj7Sh8Z\nINAoVFJSguzsbBQVFWHDhg1Ys2YNCgoKAAALFy7E/v37w94nCELQ65ycHDz55JPYsWMH7rrrLiQn\nJ2Pjxo1RjYWZBKIhYpccMOtMkAzekCkHu8+IpB4zTGavui6h/5RDVyswYcpwv4WoRLoeIVxVg9uq\nwNFpDplq8GcRbD4nOj0OTjXQqGSxWFBWVoaysrKQc7W1tQPed/z48ZBjhYWF2nRDLJhJIBoi7n6N\nleyKB+2CDzZ9+MZKiq0TSns7YGtTswkR9EtItM6LitgNxd4G2DvCNlCyecxo1+th04VpoMQFi0TD\njpkEoiHk8nnQ6XEiSWeCxWAIu4DR2WGCYYwburH9sgkJXOUwECUgi6DYOuFr6xlwwaIdHnQoEhcs\nUmKQlaBdXaO9N1Ewk0A0hDolR9ieCTY9YNcZYBfN4Xsm2NpGzIZPftpUQ7/eCKJVj54uC2wec9je\nCHavA10eB7MIRHGAQQLREPOXQ7pkLzoUN+zwhewM6W/TLLd3Q2m3qR+kEbZojocph0jHoNjboNg6\nwrZhlgQd2g0C2nVySBtmZhGI4gODBKIh1ik50OlxwOZzhnRglAQd7KIZjk4z3FYlKJug2NuGe+hD\nShG71a6STicUWye8bWLYHR8lKLArHnT6JJY9EsUZBglEF0BgNkFSZEhQYNMB7Xp9+E2fnM7eufuR\nUwqpdLWGbObk7DChu8cMO4xhN3Pq9DhhH00bXhHFOS5cJLoA/M2VbDonzDoDLIIOFkEIaa7ktvqg\nG9MDIckMQRITshQyHH+1hmLrGLB5kk0PtAs+Nk8iimPMJBBdAG6fB10eR0g2wd9cyeYxo6fLEpRN\nUGwdEZcIbn0nAAAgAElEQVRCDqeI+iOI3WoDJacTcns3vFYvnB2moOZJ/ixCh+JGp09Cp8fJ5klE\ncSbhg4SDBw8iMzMTWVlZ2v+uWbMGANDQ0ID77rsP8+bNw80334x33nlnmEdLo4nocYdsId2uk9Fu\nEMJuIa12YHRGNOUQD4sXB9NX+ugKyiLYRTPsOkPYLaFdshudcR4gEWkURf13NpafQTZ4ijcJP91Q\nV1eHb3zjG3jqqae0nbDMZjMA4KGHHkJWVhb27NmDgwcPYtWqVdi/fz+mTEn8dC7Fv8BWzRbBgDF6\nddohtFWzD7oxInQZLgi2Nihpif1BqZU+2nunGvq3YNazBTNRokj4TEJ9fT3+5V/+BRMnTkRKSgpS\nUlJwySWX4N1330VDQwOefPJJzJgxAw8++CBycnJQWVk53EOmUcQuOUKyCf5ySDuM6O4x92UTbJ1R\nlULGM3U/ChFyezdbMBMlsBERJHzpS18KOV5TU4MrrrhCyyoAQG5uLqqrqy/m8GiUi6ZVs7qfQ+KX\nQipiN2BrVdcjONxswUyUwBI+SDh9+jT+9re/4YYbbsCSJUuwZcsWeDwetLW1ITU1NejalJQUtLS0\nDNNIabTyt2ru9Ekh2QR/OaSzw6Tu59BuS/hSSKW3y6Ji61SnGtiCmShhJfSahLNnz0KSJJjNZmzd\nuhUNDQ346U9/CkmSIIoiTCZT0PUmkwluN/9jRBdXp+SAWW/sa9Us+OAQ9LDpdRgrG2AR1d0hvVYn\nDJdJ6gdsnJZCnmvBpCI5oHT29UdwW5W+Fsw6tmAmSjQJHSR84QtfwHvvvYfx48cDADIzMyHLMn74\nwx/i29/+Nrq6uoKud7vdsFgswzFUGuWCWjULblgEPcYKuqCNn7xOqI2VJFErhRxswydPywkY02Zd\nxHcRIckJpb0dilOdamALZhqRFEX99zXGexNFwk83+AMEv5kzZ8LlcmHSpEloawue27VarZg8efLF\nHB4RgMhaNXucenVdQnu72mMgAcn2Zq300dsmwiPpB2zBbPc62DyJKM4ldJDw9ttv4+qrr4bL1RfN\nHTt2DBMmTMD8+fPxySefBE0vHD58GDk5OcMxVKJztmr2SHp429Q0PcQe9QM30QSVPqpTDQO1YJZ8\nHrZgJopzCR0kzJs3D0lJSfjRj36E06dP46233sLTTz+NBx54AHl5eUhPT8djjz2Guro67Ny5E0eP\nHsXtt98+3MOmUcrfXMnmc6JDkWCHJyib0NNlgexUAElSP2gTbOtorRVzb+mj1wltqsHfgtmueNiC\nmSiBJHSQMHbsWOzatQs2mw233347Hn/8cfzbv/0b/v3f/x06nQ7PPfcc2tracNttt+HPf/4zduzY\nwUZKNGzO1arZ5dHD64S6fbQoJkSL5kD9Sx+dHSaIXkNIFoEtmIkSR0IvXATUNQi7du0Ke27atGmo\nqKi4yCMiGph/4yfJoDZXskMHi05AkkGHKR61FNLicEPvdAK2Viip3YMuXryYzlnZ0K/00e0ywQ4j\nWzATJbCEziQQJZrAVs2dPikom2CHEW6XQd3wqbf7onKOKYd42cMhXOmj29W72yNbMNNIpPRODcby\nc47qBrfbjXXr1iEvLw+LFi1CeXn5gNfu3bsXN9xwA+bOnYtly5ahpqYm6Pz8+fO1vY38+xuJohjx\n20z4TAJRorFLDph1Ji2bIMEISVDn7t0uA9xWBUZ/KWRnK5TkKXGTTRiU5FSnSQJKHx06gS2YiaK0\nefNmHDt2DBUVFWhoaEBxcTEyMjJw/fXXB11XVVWF9evXY+PGjcjJycGLL76IBx54AIcOHUJSUhJa\nWlrgcDhw8ODBoPL/pKSkiMfCTALRRTZQq2aHTkjYUkhF7FZLH9ttaitmSd/bQIktmImiIYoiKisr\nsX79emRmZqKgoAArVqzA7t27Q661Wq1YuXIlbr75ZkydOhUrV65EZ2cn6urqAACnTp3C5MmTkZGR\noe1tlJKSEtV4mEkgGgb+Vs1JOhMsBgMkGGHT6yF5+0ohdRkuCL2lkPopM4d7yINSutSpBkgSvFYv\n3K4xAVMNbMFMFKna2lr4fL6gcv3c3Fz86le/Crn2m9/8pva7y+XC7373O0yaNAlf/vKXAai7JE+f\nPv28xsMggWgYhGvVLAlGrRRyvNMdV6WQg6190EofbR1qEyUn0N1jhiTo1KkGtmAmilhbWxuSk5Nh\nMPR9PKekpMDlcsFms2HChAkh97z77ru4//77AQDPPPOMNp1QX18PURRx99134/Tp05g9ezbWrVsX\nVeDA6QaiYRLUqllxwyHIaNfrE64UUhG71WkRpxO+th54nGqXxXaDAAkKWzATRWGgfYcADLj30KxZ\ns/DKK6/g4YcfRnFxsbZ48dSpU+jq6sLKlSvx3HPPwWKx4N5774XTGfk0JjMJRMPEn00w64ww6wyw\nCz51E6QoSyGHew8HxeUAbG1QRBdkpw+OziRIir63YoMtmImiYTabQ4IB/+uBFhxOnDgREydORGZm\nJqqrq/HHP/4Rc+bMwa5du+D1erX7nnnmGeTn5+PNN9/ETTfdFNF4GCQQDaOgVs06H0TBqG0fLTvV\nckIhglLI4aJIDnU6ROuPoJY+2nUGtYGSIrMFM41MF2iDp7S0NNjtdsiyDJ1OTfZbrVZYLJaQvYqO\nHj0KvV6P2bNna8dmzpyJ+vp6AIDRaITRaNTOmUwmTJ06FS0tLREPldMNRMMosFWzpMiQBMCuM/QG\nCYrWLwGu+J1yUOxtWumjaO0rfWwXfHCCLZiJopGVlQWDwYDq6mrtWFVVFbKzs0OuraysxJYtW4KO\nffLJJ9rCxSVLluDVV1/VzjmdTpw5cwYzZsyIeDwMEoiGUWCrZie8Wimky6OHaO0thRRFKPa2cz9s\nGAxe+iizBTNRlCwWC5YuXYrS0lIcPXoUBw8eRHl5OYqKigCoWQX/poZ33nkn3nvvPVRUVODMmTPY\ntm0bjh49ql2bn5+Pbdu24f3338fJkyexdu1apKenIz8/P+LxMEggGmb+bEKnT4IEdcMnm8cMj6SH\n7HBDabf1br/cPSzjG7SyIaT0sa/Lor+BElswE0WnpKQE2dnZKCoqwoYNG7BmzRoUFBQAABYuXIj9\n+/cDAGbPno0dO3bg5ZdfxtKlS/G3v/0Nv/3tbzF58mQAwNq1a3HDDTfg0UcfxR133AFZlrFz504I\nghDxWLgmgWiY+ZsrSYoXEnyw6Yxa90Wv1QnDZZI659/VCkyInw3KzlX62KGoDaOYRSCKjsViQVlZ\nGcrKykLO1dbWBr3Oz88fMDNgMplQXFyM4uLimMfCTAJRHLBLDoiyWyuFlAQdunvM8DoBRXSpH8SD\nlEIOxx4O5yp9lBQvOj1OZhGIEhgzCURxwN3bgVEyjockKGjv3RXS49TD19YD3RecvXsjxM+ukIrL\n0TsNEr70UW3DzL4INELJChRnjP//lgff4CmeMJNAFCdcslvtKQCPtiuko9PctyukrS2+SiFdDsDe\nMWDpo83HBYtEiY5BAlGcsEsO2L0OdChutOvU7ovdPWa4rYrafdHWoW7HfBENNI2hSA4oTaehtLfD\n19aDrgYT7KIZ7QYBjYK6VwO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hMpkwdepUtLS0RPw+owoSLrnkEvzlL39BYWEhvv71r+NH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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2387be9d198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.contourf(j_grid, h_grid, np.abs(mz_result), np.arange(0, 0.5, 0.01)); \n",
    "plt.xlabel('$h$')\n",
    "plt.ylabel('$J$')\n",
    "plt.title('$M_z$ of TFI model')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Appendix\n",
    "- plot the energy curve for heisenberg model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "energies = [0.947997520997407, 0.16372943175082844, -0.35902391055941896, -1.146324328008513, -1.8240852476474292, -2.56940199901001, -3.470840054781551, -4.109763733472468, -4.755290949292606, -5.595458214637118, -6.426529223032629, -7.1571136762064675, -7.749159411441465, -8.605051718061203, -9.217393228980171, -10.049781223489374, -10.04978122348938, -10.049781223489397, -10.049781223489358, -10.049781223489347, -10.04978122348935, -10.049781223489381, -10.049781223489374, -10.049781223489374, -10.049781223489395, -10.050388105487476, -10.051291278186497, -10.05153983891799, -10.051700713349241, -10.051823153870902, -10.051852613439573, -10.05199063550094, -10.052035794005329, -10.052107041332723, -10.052279766865027, -10.05228121405697, -10.052281214056904, -10.05228121405688, -10.052281214056928, -10.052281214056936]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iIvHiBeDoCAgBZGQAxsZyV0ZERGT4Sm1XS4UKwLp1wG+/AYsWyV0NERFR6VBq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\nJ95uPyRfnx3AAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2387be9ec88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(energies, marker='s'); \n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Energy')\n",
    "plt.title('Ground state energy search for Heisenberg model')\n",
    "plt.savefig('../Img/heisenberg.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
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